91Ó°ÊÓ

The graph of each equation is a circle. Find the center and the radius, and then graph the circle. See Examples 5 through 7. $$ (x+2)^{2}+(y-3)^{2}=7 $$

Identify whether each equation, when graphed, will be a parabola, circle,ellipse, or hyperbola. Sketch the graph of each equation. If a parabola, label the vertex. If a circle, label the center and note the radius. If an ellipse, label the center. If a hyperbola, label the \(x\) - or \(y\) -intercepts. $$ y=x^{2}+4 $$

Graph each system. $$ \left\\{\begin{array}{l} x^{2}+(y-2)^{2} \geq 9 \\ \frac{x^{2}}{4}+\frac{y^{2}}{25}<1 \end{array}\right. $$

Solve each nonlinear system of equations. $$ \left\\{\begin{array}{l} x^{2}+y^{2}=16 \\ y=-\frac{1}{4} x^{2}+4 \end{array}\right. $$

The graph of each equation is a circle. Find the center and the radius, and then graph the circle. See Examples 5 through 7. $$ (x+1)^{2}+(y-2)^{2}=5 $$

Identify whether each equation, when graphed, will be a parabola, circle,ellipse, or hyperbola. Sketch the graph of each equation. If a parabola, label the vertex. If a circle, label the center and note the radius. If an ellipse, label the center. If a hyperbola, label the \(x\) - or \(y\) -intercepts. $$ y=x^{2}+12 x+36 $$

The graph of each equation is a circle. Find the center and the radius, and then graph the circle. See Examples 5 through 7. $$ x^{2}+y^{2}-4 x-8 y-2=0 $$

Solve each nonlinear system of equations. $$ \left\\{\begin{array}{l} y=\sqrt{x} \\ x^{2}+y^{2}=12 \end{array}\right. $$

Graph each system. $$ \left\\{\begin{array}{r} x^{2}-y^{2} \geq 1 \\ y \geq 0 \end{array}\right. $$

The graph of each equation is a circle. Find the center and the radius, and then graph the circle. See Examples 5 through 7. $$ x^{2}+y^{2}-2 x-6 y-5=0 $$